# A site claims to have found a formula for Ramsey's Theorem

#### Maxime

Hello to everyone, this is my first post.

My name is Maxime, I'm not really a math genius but I'm always keen to learn more about specific topics such as prime numbers and graph theory.

I'm specifically interested in Ramsey's Theorem, even made a small program which calculates any R(n,n) by brute force (although this was more a programming than a math exercise and I obviously don't intend to do any new discoveries with it).

After checking the Wikipedia entry for Ramsey's Theorem I saw several edits claiming that R(5,5) equals 46, rather than the current 43-49 bounds (no worries, none of those edits got through). I wanted to know upon which source these statements relied, after some searching I stumbled upon this website: Math Curiosities - Ramsey Theory.

Among other strong statements, the author claims to have found a formula which applies to every R(n,n): for n>2, R(n,n) = 2*((2^n) -2*n +1)

Math Curiosities said:
Please don't believe the propaganda... there's a discrete formula for a Ramsey Number. I stumbl-
ed on it after 3 hard-earned days. Contrary to what mathematicians think, finding the answer for
a particular 'n' does NOT involve a !HUGE AMOUNT! of calculations.
Propaganda? What propaganda? Anyway...

Math Curiosities said:
I found that the formula, for n> 2, is R(n,n)= 2*((2^n) -2*n +1), or... n:R(n,n),... 3:6,...4:18,...5:46, etc.
Only one 'charitable' (or solution) matrix and one 'equitable' (or counter-example) matrix, both ad-
hering to Ramsey's idea of chaotic randomness, need to be checked for each answer.
An example of a 'charitable' and 'equitable' matrix is provided on the website.

Math Curiosities said:
You'll find comfort in this solution without any implicit confusion.
:?

Now for my question: this solution looks way too easy to be true, so I'm wondering if someone on this forum can find the flaw(s) in the authors' logic. I didn't find any, but then again I'm not an expert in this.

I'm starting my studies for my masters degree in computer science at the end of the month, it contains some challenging math so I'll definitely be very active in here! Cheers.

#### CRGreathouse

Forum Staff
Re: A site claims to have found a formula for Ramsey's Theor

Maxime said:
Now for my question: this solution looks way too easy to be true, so I'm wondering if someone on this forum can find the flaw(s) in the authors' logic. I didn't find any, but then again I'm not an expert in this.
I've seen this beforw. It looks pretty crackpot, very hard to follow anything. I'm not sure if it's precise enough to locate a unique "first flaw".

Maxime said:
I'm starting my studies for my masters degree in computer science at the end of the month, it contains some challenging math so I'll definitely be very active in here! Cheers.
Welcome!